Remarks on the locality of generalized global symmetries

We examine generalized global symmetries as a kind of compactly supported cohomology, and so are led to revisit questions about the locality of quantum field theory, following Segal. Physics naturally suggests a generalization of factorization algebras, aimed at capturing nonperturbative information, and we explain how higher group symmetries offer examples of this generalization, providing an extension of the nonabelian Poincaré duality of Salvatore and Lurie. Finally, we explore how continuous generalized symmetries and anomalies can be cast in this framework.